In a regression setting with functional covariates, it is of paramount importance to estimate coefficient functions that are interpretable. 

We develop a framework to estimate locally sparse functions which are exactly zero in a subset of positive Lebesgue measure of their 

domain. We achieve this by combining the B-splines basis with the Overlap Group Lasso penalty, a generalization of the L₂ penalty 

which allows groups to have common elements. The corresponding optimization problem is solved using the Alternating Direction 

Method of Multipliers (ADMM) algorithm. The advantage of the proposed method over classical approaches is clearly stated and further 

supported by simulations and some case-studies, for both scalar and functional response regression models.